Selected quad for the lemma: end_n

Word A	Word B	Word C	Word D	Occurrence	Frequency Band	MI	MI Band	Prominent
end_n	draw_v	line_n	perpendicular_a	3,095	5	14.0786	5	true

Text snippets containing the quad

ID	Title	Author	Corrected Date of Publication (TCP Date of Publication)	STC	Words	Pages
A32712	Physiologia Epicuro-Gassendo-Charltoniana, or, A fabrick of science natural, upon the hypothesis of atoms founded by Epicurus repaired [by] Petrus Gassendus ; augmented [by] Walter Charleton ...	Charleton, Walter, 1619-1707.; Epicurus.; Gassendi, Pierre, 1592-1655.	1654 (1654)	Wing C3691; ESTC R10324	556,744	505

this invented by Gassendus Thirdly we may account the Line DE for the first degree of Velocity acquired in the end of the first time insomuch as the first time AE is not individual but may be divided into so many instants or shorter times as there are points or particles in the line AE or AD so neither is the degree of Velocity individual or wholly acquired in one instant but from the beginning encreaseth through the whole first time and may be repraesented by so many Lines as may be drawn parallel to the Line DE betwixt the points of the Lines AD and AE so that as those Lines do continually encrease from the point A to the Line DE so likewise doth the Velocity continually encrease from the beginning of the motion and being represented what it is in the intercepted instants of the first time by the intercepted Lines it may be represented what it is in the last instant of the same first time by the Line DE drawn betwixt the two last points of the Triangle ADE And because the Velocity thenceforward continuing its Encrease may be again signified by Greater and Greater Lines continently drawn betwixt all the succeeding points of the remaining Lines DB and EC hence comes it that the Line FG doth represent the degree of Velocity acquired in the end of the second moment the Line HI the Velocity acquired in the end of the third moment and the Line KL the velocity acquired in the end of the fourth moment And evident it is from hence how the velocities respond in proportions to the Times since by reason of the Triangles of a common angle and parallel bases it is well known that as DE are to EA so FG to GA HI to IA and KL to LA. Thus keeping your eye upon the Figure and your mind upon the Analogy you shall fully comprehend that in the first moment of Time the falling stone doth acquire one degree of Velocity and pervades one degree of space that in the second moment of Time it acquires another degree of Velocity which being conjoynd to the former makes two and in the mean while three spaces are pervaded that in the third moment it acquires another degree of Velocity which conjoyned to the two former makes three and in the mean while seven parts of space are pervaded and so forward You shall fully comprehend also that the Celerities obtain the same Ration as the moments of Time and that the spaces pervaded from the beginning to the end of the motion have the same Ration as the Quadrates of the moments of Time which we assumed to Demonstrate out of Gassendus But still it concerns you to remember that we here discourse of that Motion which is Equally or Uniformly Accelerated or whose velocity doth continually and uniformly encrease nor is there any moment of the consequent time in which the motion is not more swift than it was in every antecedent moment and in which it is not accelerated according to the same Reason For the want of this Advertisement in chief seems to have been the unhappy occasion of that great trouble the Learned Jesuit Petrus Cazraeus put Gassendus to in his two Epistles De Proportione qua Gravia decidentia accelerantur And this kindly conducts us to the Physical Reason of this Proportion in which the velocity of bodies Descending is observed to encrease For wholly excluding the supposition of the Aers assistance of the Downward motion of a stone by recurring above and so impelling it downward and admitting the Magnetick Attraction of the Earth to be the sole Cause of its Descent unto both which the considerations formerly alleadged seem to oblige us it is familiar for us to conceive that the Increment of its Celerity according to the proportion assigned ariseth from hence While in the first moment the earth attracts the stone one degree of Celerity is acquired and one degree of space is pervaded In the second moment the attraction of the Earth continuing another degree of celerity is acquired and three equal spaces are pervaded one by reason of the degree of celerity in the mean while acquired and two by reason of the degree of celerity formerly acquired and still persevering as that which is doubly ●equivalent to the new degree in the mean while acquired because it is Complete and entire from the very beginning of the 2d moment but the other is only acquiring or in fieri and so not complete till the end of the second moment Then according to the same Ration in the third moment another degree of celerity is acquired and five spaces equal are pervaded one by reason of the new degree of celerity in the mean while acquired and fower by reason of the two former persevering i. e. two in each moment praecedent or one of a duplicate aequivalency to the new one not yet complete Then in the fourth moment another degree of celerity is acquired and seven spaces are pervaded one by reason of the fresh degree in the interim acquired and six by reason of the three former per●●vering i. e. two in each praecedent moment And so of the rest through the whole motion computing the degrees of encreasing Celerity by the ration of Quadrate Numbers Now many are the Physical Theorems and of considerable importance which might be genuinely deduced from this excellent and fruitful Physicomathematical speculation and as many the admired Apparences in nature that offer themselves to be solved by Reasons more than hinted in the same but such is the strictness of our method and weariness of our Pen that we can in the praesent make no farther advantage of it than only to infer from thence the most probable Reason of that so famous Phaenomenon The equal velocity of two stones or bullets the one of 100 pound the other of only one ounce weight descending from the same altitude experience constantly attesting that being dropt down together or turned off in the same instant from the top of a tower the Lesser shall arrive at the ground as soon as the Greater For this admirable Effect seems to have no other Cause but this that the Lesser body as it containeth fewer parts so doth it require the Impulses or strokes of fewer Magnetical rays by which the attraction is made and such is the proportion of the two forces as that each moveable being considered with what Resistence you please still is the force in the movent equally sufficient to overcome that resistence and a few magnetique rays suffice to the attraction of a few parts as well as many to the attraction of many parts So that the space being equal which both are to pervade it follows that it must be pervaded by both in equal or the same time Provided always that the two bodies assumed be of the same matter for in case they be of divers matters as the one of Wood the other of Iron or Lead that may cause some small

crescant iterum quaenam enim Elateria cogunt aerem ad sui restitutionem How do those Vacuities minute in the aer when enlarged by rarefaction recover their primitive exility and when diminished by condensation re-expand themselves to their former dimensions What Elaters or Springs are in the aer which may cause its suddain restitution to its natural constitution of insensible particles We Answer that as it is the most catholique Law of Nature for every thing so much as in it lies to endeavour the conservation of its originary state so in particular it is the essential quality of the Aer that its minute particles conserve their natural Contexture and when forced in Rarefaction to a more open order or in Condensation to a more close order immediately upon the cessation of that expanding or contracting violence to reflect or restore themselves to their due and natural contexture Nor need the Aer have any Principle or Efficient of this Reflection other then the Fluidity or Confluxibility of its Atomical Parts the essence or Quiddity of which Quality we must reserve for its proper place in our ensuing theory of Qualities CHAP. V. A Vacuum Praeternatural SECT I. BEsides a Natural or Disseminate Vacuity frequently intercepted betwixt the incontiguous Particles of Bodies the Argument of our immediately precedent Chapter not a few of the highest form in the school of Democritus have adventured to affirm not only the possibility but frequent introduction of a Praeternatural or Coacervate Inanity such as may familiarly be conceived if we imagine many of those minute inane spaces congregated into one sensible void space To assist this Paradox the autoptical testimony of many Experiments hath been pleaded especially of that Glass Fountain invented by Hero praef in Spirit and fully described by the learned and industrious Turnebus in lib. de calore and of that Brass Cylindre whose concave carries an Embolus or sucker of wood concerning which the subtle Galilaeo hath no sparing discourse in the first of his Dialogues but above all of that most eminent and generally ventilated one of a Glass Cylindre or Tube filled with Quicksilver and inverted concerning which not long after the invention thereof by that worthy Geometrician Torricellius at Florence have many excellent Physicomathematical Discourses been written by Monsieur Petit Dr. Paschal Mersenn●s Gassendus Stephanus Natalis Who being all French seemed unanimously to catch at the experiment as a welcom opportunity to challenge all the Wits of Europe to an aemulous combat for the honour of perspicacity Now albeit we are not yet fully convinced that the chief Phaenomenon in this illustrious Experiment doth clearly demonstrate the existence of a Coacervate Vacuity such as is thereupon by many conce●ed and with all possible subtlety defended by that miracle of natural Science the incomparable Mersennus in reflexionib Physicomathemat yet insomuch as it affords occasion of many rare and sublime speculations whereof some cannot be solved either so fully or perspicuously by any Hypothesis as that of a Vacuum Disseminatum among the insensible particles of Aer and Water and most promise the pleasure of Novelty if not the profit of satisfaction to the worthy considerer we judge it no unpardonable Digression here to present to our judicious Reader a faithful Transcript of the Experiment together with the most rational solutions of all the admirable Apparences observed therein first by Torricellius and the rest beyond Sea and since more then once by our selves The Experiment Having praepared a Glass Tube whose longitude is 4 feet and the diameter of its concavity equal to that of a mans middle finger and stopped up one of its extremities or ends with a seal Hermetical fill it with Quicksilver and stop the other extreme with your middle finger Then ha●ing with a most slow and gentle motion lest otherwise the great weight of the Quicksilver break it inverted the Tube immerge the extreme stopt by your finger into a Vessel filled with equal parts of Quicksilver and Water not withdrawing your finger untill the end of the Tube be at least 3 or 4 inches deep in the subjacent Quicksilver for so you praevent all insinuation or intrusion of Aer This done and the Tube fixed in an erect or perpendicular position upon the subduction of your finger from the lower orifice you may observe part of the Quicksilver contained in the Tube to descend speedily into the restagnant or subjacent Quicksilver leaving a certain space in the superior part of the Tube according to apparence at least absolutely Void or Empty and part thereof after some Reciprocations or Vibrations to remain still in the Tube and possess its cavity to a certain proportion or altitude of 27 digits or 2 feet 3 digits and an half proximè constantly Further if you recline with a gentle motion also the upper extreme of the Tube untill the lower formerly immersed in the Quicksilver arise up into the region of the Water incumbent on the surface of the Quicksilver you may perceive the Quicksilver remaining in the Tube to ascend by sensible degrees up to the superior extreme thereof together with part of the Water both those liquors to be confounded together and at length the Quicksilver wholly to distill down in parcels surrendring the cavity of the Tube to the possession of the Water Likewise if you recline the superior extreme of the Tube untill its altitude respond to that of 27 digits still retaining the opposite extreme in the region of the subjacent Quicksilver in the vessel then will the Quicksilver be sensibly impelled up again into the Tube untill that space formerly vacated be replenished Finally if when t●e Quicksilver hath fallen down to the altitude of 27 digits the Tube be suddainly educed out of the subjacent Quicksilver and Water so as to arrive at the confines of the Aer then doth the Aer rush into the Tube below with such impetuosity as to elevate the Quicksilver and Water contained in the Tube to the top nay to blow up the sealed end thereof and drive out the liquors 4 or 5 feet perpendicular up in the aer not without some terror though not much danger to the Experimentator especially if he do not expect it Now though it be here praescribed that the Tube ought to be 4 feet in length and the amplitude of its Cavity equal to that of an ordinary mans finger yet is neither of these necessary For whatever be the longitude and whatever the amplitude of the Tube still doth the Quicksilver after various reciprocations acquiesce and subsist at the same standard of 27 digits as Dr Paschal junior found by experience in his Tube 15 feet long which he bound to a spear of the same length so to prevent the fraction thereof when it was erected perpendicularly replete with Quicksilver in libro cui titulus Experiences Novelles touchant le Vuide Among those many Natalis reckons up no less then 20 stupendious Magnalities or rare Effects